{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VISKQPDW4DMHPOE4NR6KRN2LJE","short_pith_number":"pith:VISKQPDW","schema_version":"1.0","canonical_sha256":"aa24a83c76e0d877b89c6c7ca8b74b49122adc4c24519964b1ad9dffb3ea83e1","source":{"kind":"arxiv","id":"1001.0733","version":2},"attestation_state":"computed","paper":{"title":"Heisenberg double H(B^*) as a braided commutative Yetter-Drinfeld module algebra over the Drinfeld double","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"AM Semikhatov","submitted_at":"2010-01-03T16:46:12Z","abstract_excerpt":"We study the Yetter--Drinfeld D(B)-module algebra structure on the Heisenberg double H(B^*) endowed with a \"heterotic\" action of the Drinfeld double D(B). This action can be interpreted in the spirit of Lu's description of H(B^*) as a twist of D(B). In terms of the braiding of Yetter--Drinfeld modules, H(B^*) is braided commutative. By the Brzezinski--Militaru theorem, H(B^*)#D(B) is then a Hopf algebroid over H(B^*). For B a particular Taft Hopf algebra at a 2p-th root of unity, the construction is adapted to yield Yetter--Drinfeld module algebras over the 2p^3-dimensional quantum group U_q(s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1001.0733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-01-03T16:46:12Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"1f8f3df64007b9200ead9b080330015f1560738de31f000ee101097dd14b08ea","abstract_canon_sha256":"0e5132f65cdc8128982ee37617082162adafbfe4189859b24ffad1144104e368"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:18.801182Z","signature_b64":"shSFjbs2UfRqxb8tEYOp05PwrYtCwBrtlYcXdbDimU/8BE1YHzncTJUYypMxPj0gnziuiNYpgakHDANp4xzhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa24a83c76e0d877b89c6c7ca8b74b49122adc4c24519964b1ad9dffb3ea83e1","last_reissued_at":"2026-05-18T04:12:18.800589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:18.800589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heisenberg double H(B^*) as a braided commutative Yetter-Drinfeld module algebra over the Drinfeld double","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"AM Semikhatov","submitted_at":"2010-01-03T16:46:12Z","abstract_excerpt":"We study the Yetter--Drinfeld D(B)-module algebra structure on the Heisenberg double H(B^*) endowed with a \"heterotic\" action of the Drinfeld double D(B). This action can be interpreted in the spirit of Lu's description of H(B^*) as a twist of D(B). In terms of the braiding of Yetter--Drinfeld modules, H(B^*) is braided commutative. By the Brzezinski--Militaru theorem, H(B^*)#D(B) is then a Hopf algebroid over H(B^*). For B a particular Taft Hopf algebra at a 2p-th root of unity, the construction is adapted to yield Yetter--Drinfeld module algebras over the 2p^3-dimensional quantum group U_q(s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0733","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1001.0733","created_at":"2026-05-18T04:12:18.800697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0733v2","created_at":"2026-05-18T04:12:18.800697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0733","created_at":"2026-05-18T04:12:18.800697+00:00"},{"alias_kind":"pith_short_12","alias_value":"VISKQPDW4DMH","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VISKQPDW4DMHPOE4","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VISKQPDW","created_at":"2026-05-18T12:26:15.391820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE","json":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE.json","graph_json":"https://pith.science/api/pith-number/VISKQPDW4DMHPOE4NR6KRN2LJE/graph.json","events_json":"https://pith.science/api/pith-number/VISKQPDW4DMHPOE4NR6KRN2LJE/events.json","paper":"https://pith.science/paper/VISKQPDW"},"agent_actions":{"view_html":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE","download_json":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE.json","view_paper":"https://pith.science/paper/VISKQPDW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0733&json=true","fetch_graph":"https://pith.science/api/pith-number/VISKQPDW4DMHPOE4NR6KRN2LJE/graph.json","fetch_events":"https://pith.science/api/pith-number/VISKQPDW4DMHPOE4NR6KRN2LJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE/action/storage_attestation","attest_author":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE/action/author_attestation","sign_citation":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE/action/citation_signature","submit_replication":"https://pith.science/pith/VISKQPDW4DMHPOE4NR6KRN2LJE/action/replication_record"}},"created_at":"2026-05-18T04:12:18.800697+00:00","updated_at":"2026-05-18T04:12:18.800697+00:00"}